Alternating Circulant Random Features for Semigroup Kernels

Authors

  • Yusuke Mukuta The University of Tokyo
  • Yoshitaka Ushiku The University of Tokyo
  • Tatsuya Harada The University of Tokyo and RIKEN AIP

Abstract

The random features method is an efficient method to approximate the kernel function. In this paper, we propose novel random features called "alternating circulant random features,'' which consist of a random mixture of independent random structured matrices. Existing fast random features exploit random sign flipping to reduce the correlation between features. Sign flipping works well on random Fourier features for real-valued shift-invariant kernels because the corresponding weight distribution is symmetric. However, this method cannot be applied to random Laplace features directly because the distribution is not symmetric. The method proposed herein yields alternating circulant random features, with the correlation between features being reduced through the random sampling of weights from multiple independent random structured matrices instead of via random sign flipping. The proposed method facilitates rapid calculation by employing structured matrices. In addition, the weight distribution is preserved because sign flipping is not implemented. The performance of the proposed alternating circulant random features method is theoretically and empirically evaluated.

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Published

2018-04-29

How to Cite

Mukuta, Y., Ushiku, Y., & Harada, T. (2018). Alternating Circulant Random Features for Semigroup Kernels. Proceedings of the AAAI Conference on Artificial Intelligence, 32(1). Retrieved from https://ojs.aaai.org/index.php/AAAI/article/view/11674